From: Andrew Lorimer <andrew@lorimer.id.au>
Date: Tue, 26 Mar 2019 22:44:24 +0000 (+1100)
Subject: [spec] rates
X-Git-Tag: yr12~180
X-Git-Url: https://git.lorimer.id.au/notes.git/diff_plain/4c492006f24c2d8629f148886b9a83db70dec3e2?hp=ff236897195c8e927268e51ea469dbf46591e75f

[spec] rates
---

diff --git a/spec/calculus.md b/spec/calculus.md
index ee88068..c59c4b7 100644
--- a/spec/calculus.md
+++ b/spec/calculus.md
@@ -245,3 +245,15 @@ $\int k f(x) dx = k \int f(x) dx$
 
 To find stationary points of a function, substitute $x$ value of given point into derivative. Solve for ${dy \over dx}=0$. Integrate to find original function.
 
+## Rates
+
+### Related rates
+
+$${da \over db} \quad \text{change in } a \text{ with respect to } b$$
+
+#### Gradient at a point on parametric curve
+
+$${dy \over dx} = {{dy \over dt} \over {dx \over dt}} \> \vert \> {dx \over dt} \ne 0$$
+
+$${d^2 \over dx^2} = {d(y^\prime) \over dx} = {{dy^\prime \over dt} \over {dx \over dt}} \> \vert \> y^\prime = {dy \over dx}$$
+